Find the value of $a^{2} + b^{2}$ if $a + b = 5$ and $a b = 3$

Open in App

Solution

${(a + b)}^{2} = a^{2} + b^{2} + 2 a b$

$\Rightarrow a^{2} + b^{2} = {(a + b)}^{2} - 2 a b$

$\Rightarrow a^{2} + b^{2} = {(5)}^{2} - 2 \times 3$

$\Rightarrow a^{2} + b^{2} = 25 - 6 = 19$

$∴ a^{2} + b^{2} = 19$

Suggest Corrections

Similar questions

a = \frac{\sqrt{5} + 1}{\sqrt{5} - 1}

b = \frac{\sqrt{5} - 1}{\sqrt{5} + 1}

\frac{a^{2} + a b + b^{2}}{a^{2} - a b + b^{2}}

If a + b = 10 and ab = 16, find the value of $a^{2} - a b + b^{2} a n d a^{2} + a b + b^{2}$ .

a - b = 5

a^{2} + b^{2} = 53

a b

a = 3, b = - 3

a^{2} + a b + b^{2}

Join BYJU'S Learning Program